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Proof analysis in intermediate logics

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Abstract

Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than in the explanation of the rules.

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Authors and Affiliations

  1. School of Computer Science, St. Andrews University, St. Andrews, Fife, KY16 9SX, Scotland

    Roy Dyckhoff

  2. Department of Philosophy, University of Helsinki, P.O. Box 24, Unioninkatu 40A, 00014, Helsinki, Finland

    Sara Negri

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  1. Roy Dyckhoff
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  2. Sara Negri
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Correspondence to Roy Dyckhoff.

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Dyckhoff, R., Negri, S. Proof analysis in intermediate logics. Arch. Math. Logic 51, 71–92 (2012). https://doi.org/10.1007/s00153-011-0254-7

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